Overview

This document contains some analysis of the previously cleaned seed data.

This analysis was performed using R version 4.4.1 (2024-06-14 ucrt). The tidyverse suite of packages was used for data manipulation and visualisation. The emmeans package was used for model predictions.

Data Loading

The cleaned data is read in. There is the full dataset followed by the dataset that has been summarised (over the unbalanced reps).


## tibble [4,316 × 15] (S3: tbl_df/tbl/data.frame)
##  $ Year                    : Factor w/ 3 levels "2021-2022","2022-2023",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ Farm                    : Factor w/ 19 levels "Ahuriri","Ashford 1",..: 6 6 6 6 6 6 6 6 6 6 ...
##  $ Property_Grouping       : Factor w/ 18 levels "Ahuriri","Ashford_1",..: 6 6 6 6 6 6 6 6 6 6 ...
##  $ PK_Boundary             : Factor w/ 10 levels "Bare_fence","Control_farm",..: 1 1 1 1 1 1 1 2 2 2 ...
##  $ Simplified_Boundary     : Factor w/ 4 levels "Old native","New native",..: 3 3 3 3 3 3 3 4 4 4 ...
##  $ Very_Simplified_Boundary: Factor w/ 2 levels "Bare_fence","Mixed_native": 1 1 1 1 1 1 1 1 1 1 ...
##  $ Planting_date           : chr [1:4316] "*" "*" "*" "*" ...
##  $ Treatment               : Factor w/ 3 levels "Hand pollinated",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ Colour                  : logi [1:4316] NA NA NA NA NA NA ...
##  $ Rep                     : num [1:4316] 2 2 2 2 1 1 1 2 2 2 ...
##  $ Number_of_Pods          : chr [1:4316] "10" "10" "10" "10" ...
##  $ Pod_number              : chr [1:4316] "7" "10" "3" "1" ...
##  $ Seed viable             : num [1:4316] 13 12 12 10 13 15 16 16 11 12 ...
##  $ Seed inviable           : num [1:4316] 0 0 1 0 0 0 0 0 0 0 ...
##  $ Type_of_farm            : Factor w/ 2 levels "Arable","Dairy": 2 2 2 2 2 2 2 2 2 2 ...


Next the previously saved summarised data is loaded.


## tibble [319 × 6] (S3: tbl_df/tbl/data.frame)
##  $ Year               : Factor w/ 3 levels "2021-2022","2022-2023",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ Farm               : Factor w/ 19 levels "Ahuriri","Ashford 1",..: 1 1 1 1 1 2 2 2 2 2 ...
##  $ Type_of_farm       : Factor w/ 2 levels "Arable","Dairy": 1 1 1 1 1 2 2 2 2 2 ...
##  $ Simplified_Boundary: Factor w/ 4 levels "Old native","New native",..: 2 2 2 4 4 2 2 2 4 4 ...
##  $ Treatment          : Factor w/ 3 levels "Hand pollinated",..: 1 2 3 1 2 1 2 3 1 2 ...
##  $ Mean_seeds_viable  : num [1:319] 16.2 14.8 1 16.2 10.4 ...


Next we further summarise the data and calculate the means for each Year, Simplified_Boundary and Treatment combination (the black dots in the second and third graphs below).

Graphs

With the farms shown


The details of the particular farms is not of interest so we remove this information and add the overall means to the plots.

With the overall raw means

The two plots below are the same, just with minor differences (HP abbreviation and the size of the points).



Dairy or Arable added to the graphs

First we look at the data in a single graph and then with the farm types separated.


Modelling

Comments

  • We remove the Control farms and the Closed treatment so we can see if there is a difference between HP and Open.
  • Fitting a zero-inflated model with the Closed treatment data included did not converge. Since this was not the “main comparison of interest” I did not spend a lot time trying to make it work.
  • The data is separated into Arable and Dairy for modelling purposes.
  • Again I ran into problems with trying to fit a single model.

Model descriptions

We fit linear mixed-effect models to the two sets of data. The response is Mean_seeds_viable. The fixed-effects are Treatment and Simplified_Boundary plus their two-way interaction. Year is not really of interest (I hope?) so we make it a random effect. There is also a random effect for Farm nested in Year. This means that there are 3 levels to the Year random effect, and 24 for the Farm:Year random effect (and it doesn’t matter that we don’t have data from every farm for each year).

Graphs of data used in models

Results Arable farms

Two outliers were removed from the data to better satisfy modelling assumptions.

If the outliers are included in the model, the story is the same (results not shown).

The ANOVA table is:


Chisq Df Pr(>Chisq)
Treatment 70.52435 1 0.000000
Simplified_Boundary 20.66522 2 0.000033
Treatment:Simplified_Boundary 15.83355 2 0.000365


The two-way interaction is significant. The modelled/predicted means and 95% confidence intervals are graphed and given in a table. Note that the post-hoc pairwise comparison p-values were adjusted using the False Discovery Rate (FDR) correction to account for multiple tests.


Simplified_Boundary Treatment Predicted mean lower.CL upper.CL
Old native Hand pollinated 17.05 8.97 25.13
New native Hand pollinated 18.02 9.80 26.24
Bare fence Hand pollinated 17.01 8.77 25.25
Old native Open 15.87 7.79 23.95
New native Open 15.28 6.93 23.63
Bare fence Open 12.52 4.41 20.64 


## Treatment = Hand pollinated:
##  contrast                estimate    SE   df t.ratio p.value
##  Old native - New native  -0.9725 0.673 67.3  -1.444  0.2301
##  Old native - Bare fence   0.0333 0.598 50.5   0.056  0.9558
##  New native - Bare fence   1.0058 0.646 65.9   1.558  0.2301
## 
## Treatment = Open:
##  contrast                estimate    SE   df t.ratio p.value
##  Old native - New native   0.5961 0.663 67.6   0.899  0.3718
##  Old native - Bare fence   3.3524 0.613 51.1   5.465  <.0001
##  New native - Bare fence   2.7563 0.646 65.9   4.269  0.0001
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: fdr method for 3 tests


The table above shows pairwise Simplified_Boundary comparisons for each of the Treatments. There is no difference for Hand pollinated. For Open the New native and Old native each have approximately 3 more viable seeds on average than the Bare fence. There is no difference between New native and Old native.

Results Dairy farms

The ANOVA table is:


Chisq Df Pr(>Chisq)
Simplified_Boundary 25.565 2 0.000
Treatment 32.257 1 0.000
Simplified_Boundary:Treatment 9.679 2 0.008


The two-way interaction is significant. The modelled/predicted means and 95% confidence intervals are graphed and given in a table.


Simplified_Boundary Treatment Predicted mean lower.CL upper.CL
Old native Hand pollinated 17.68 10.29 25.07
New native Hand pollinated 17.37 11.46 23.29
Bare fence Hand pollinated 16.64 9.81 23.48
Old native Open 16.43 9.04 23.82
New native Open 15.11 9.20 21.03
Bare fence Open 12.30 5.46 19.13 


## Treatment = Hand pollinated:
##  contrast                estimate    SE   df t.ratio p.value
##  Old native - New native    0.303 0.896 79.5   0.338  0.7363
##  Old native - Bare fence    1.033 0.719 67.8   1.437  0.4664
##  New native - Bare fence    0.730 0.935 77.1   0.781  0.6559
## 
## Treatment = Open:
##  contrast                estimate    SE   df t.ratio p.value
##  Old native - New native    1.315 0.896 79.5   1.467  0.1464
##  Old native - Bare fence    4.132 0.719 67.8   5.747  <.0001
##  New native - Bare fence    2.818 0.935 77.1   3.014  0.0052
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: fdr method for 3 tests


The table above shows pairwise Simplified_Boundary comparisons for each of the Treatments. There is no difference for Hand pollinated.

For Open, the New native have approximately 3 more viable seeds on average than the Bare fence. The Old native have approximately 4 more viable seeds on average than the Bare fence. There is no difference between New native and Old native.